R10. IV B.Tech II Semester Regular Examinations, April/May DIGITAL CONTROL SYSTEMS JNTUK

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1 Set No. 1 1 a) Explain about the shifting and scaling operator. b) Discuss briefly about the linear time invariant and causal systems. 2 a) Write the mapping points between S-Plane and Z-plane. b) Find the z-transform of (i) unit step (ii) f(t)=t e -at 3 a) Explain about the weighted resistor 3 bit D/A converter? b) Explain any examples of data control systems? 4 a) What are the methods for computation of state transition matrix. Explain any one method? b) A discrete time system is described by the differential equation assuming initial conditions are y(0) = 1, y(1) = 0, T = 1 sec. Find the state transition matrix. 5 a) Explain the Duality between controllability and observability. b) Consider that a digital control system is described by the state equation. system., Determine the controllability of the 6 a) Explain the following mapping between the S-Plane and the Z-Plane. (i) Primary strips and complementary Strips (ii) Constant frequency loci (iii) Constant damping ratio loci b) Explain the stability conditions of closed loop systems in the Z over in the S- plane. [12] [3] 7 a) Write the transient response specifications? b) Explain the design procedure in the w-plane? 8 a) Discuss the necessary conditions for design of state feedback controller [10] through pole placement? b) Explain about the state observers? [5]

2 Set No. 2 1 Explain in detail about the periodic and nonperiodic signals with a neat sketch? [15] 2 a) Solve the following difference equation [5] b) Obtain the z transform of [5] c) Find the inverse z-transform of F(Z) = [5] 3 a) State and prove the sampling theorem? b) Derive transfer functions for the following data hold circuits. (i) Zero order hold circuit (ii) First order hold circuit 4 a) Write the controllable and diagonal canonical forms? b) Consider a discrete linear data control system, whose input-output relation is described by the difference equation initial conditions are. Test the state controllable and observable canonical forms? 5 a) Explain the concepts of controllability and observability. b) Investigate the controllability and observability of the digital system. 6 a) List the difference between the Jury stability test and stability analysis using bilinear transformation coupled with routh stability criterion? b) Consider the discrete time unity feedback control system (T=1 sec) whose open loop pulse transfer function is given by and Determine the range of K for stability by use of the Jury stability test. 7 a) Discuss about the response of a linear time invariant discrete time system to a sinusoidal input? b) Consider the system defined by u(kt) is the input and x(kt) the output. Obtain the steady state output x(kt), when the input u(kt) is the sampled sinusoidal. 8 Derive the necessary and sufficient conditions for design of state feedback controller through pole placement? [15]

3 1 Discuss in detail about the continuous and discrete time signals with neat sketches? 2 a) Obtain the Z-transform of the following (i) (ii) where a is constant b) Consider where obtain the inverse Z-transform of 3 a) What are the various types of analog to digital converters? Explain successive approximation type analog to digital converters with neat schematic diagram? b) Describe the sample and hold operations? 4 a) Write the state transition matrix and its properties? b) Obtain the state transition matrix of the following discrete time system 5 a) Explain the test for controllability and observability. b) Given the system x (k+1)=ax (k)+bu(k) y(k)=c x(k) Set No. 3 Determine the state controllability of the system. 6 a) State and explain the jury stability test. b) Using Jury s stability criterion find the range of K, for which the characteristic equation is closed loop stable. 7 a) Explain the relation between the bilinear transformation and the w plane? b) Discuss the review of phase lag, lead and lag-lead compensator? 8 a) Explain the sufficient conditions for design of state feedback controller through pole placement? b) Derive the ackerman s formula? [15]

4 Set No. 4 1 a) Explain about the discrete time signals with a neat sketch? b) Describe about the nonperiodic signals with a neat sketch? 2 a) State and prove the following Z-Transform theorems (i) Shifting theorem (left & right) (ii) Initial value theorem (iii) Final value theorem b) Find the Z-transform of the following (i) (ii) 3 a) What are the advantages of sampling process in control systems? [5] b) Explain any two types of digital to analog converters with a neat circuit? [10] 4 a) What are the state space representation forms and explain them. b) Consider the following system. = Obtain the state space representation forms of controllable and observable canonical forms. 5 a) Derive the necessary condition for the digital control system X(K+1) = AX(K)+Bu(K) C(k) = DX(K) to be observable. b) Examine whether the discrete data system Is (i) state controllable (ii) output controllable and (iii) observable. 6 a) Discuss the stability analysis of discrete control system using (i) Routh stability criteria (ii) Bilinear transformation b) Using Jury s stability criterion, determine the stability of the following discrete time systems (i) (ii) 1 of 2

5 Set No. 4 7 a) Explain about the digital PID controllers with neat sketch? [10] b) Consider the transfer function system shown. The sampling period T is assumed to be 0.1 sec. obtain G(w). 8 a) Explain the concept of state feedback controllers? [5] b) Consider the system Determine a suitable state feedback gain matrix k such that the system will have the closed loop poles at [5] [10] 2 of 2

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